Latent instabilities in metallic LaNiO3 films by strain control of Fermi-surface topology

Strain control is one of the most promising avenues to search for new emergent phenomena in transition-metal-oxide films. Here, we investigate the strain-induced changes of electronic structures in strongly correlated LaNiO3 (LNO) films, using angle-resolved photoemission spectroscopy and the dynamical mean-field theory. The strongly renormalized eg-orbital bands are systematically rearranged by misfit strain to change its fermiology. As tensile strain increases, the hole pocket centered at the A point elongates along the kz-axis and seems to become open, thus changing Fermi-surface (FS) topology from three- to quasi-two-dimensional. Concomitantly, the FS shape becomes flattened to enhance FS nesting. A FS superstructure with Q1 = (1/2,1/2,1/2) appears in all LNO films, while a tensile-strained LNO film has an additional Q2 = (1/4,1/4,1/4) modulation, indicating that some instabilities are present in metallic LNO films. Charge disproportionation and spin-density-wave fluctuations observed in other nickelates might be their most probable origins.


S1. Lattice structures of LaNiO3 films
We monitored surface crystal structures of LaNiO3 (LNO) films using in situ reflection high-energy electron diffraction as shown in Figs. S1(a) and S1(b). They show a 1×1 surface crystal structure, and no additional structure is observed. Figures S1(c)−(e) show x-ray diffraction data for thirty-unit cell (UC)-thick LNO films on LaAlO3 (LAO, −1.3% misfit strain) and SrTiO3 (STO, +1.7% misfit strain) substrates. The data were obtained using a high-resolution six-circle x-ray diffractometer at the 9C Beamline of PLS. We are able to obtain c-lattice parameters from θ-2θ measurements. All the films show well-defined Kiessig fringes indicating the uniform film thickness and atomically smooth interfaces, surfaces of the LaNiO3 films. Additionally, we confirmed that the LNO films are fully and homogeneously strained over 30 UC, based on the reciprocal space mapping in the (103) plane. Additionally, we calculate the c-lattice parameters of LNO films assuming a fixed unitcell volume for a pseudocubic bulk LNO (a = 3.84 Å). As shown in Fig. S1(f), compared with the calculated values, the measured c-lattice parameter in the LNO/LAO exhibits a small decrease and that in the LNO/STO exhibits a large increase. These results indicate that the unit-cell volumes of the LNO films are changed depending on the misfit strain.
To understand this volume change in the strained LNO films, we obtained the lattice structure using the generalized gradient approximation (GGA) calculations. To apply the biaxial strain caused by epitaxial growth on the lattice mismatched substrates, the cubic cell was deformed by −1.7% (+2.0%) along the a and b directions to account for compressive (tensile) strain, as shown in Figs. S1(g) and S1(h). The system is allowed to relax along the c direction to minimize the total energy to within 0.0001 Ry. Distortion of the oxygen octahedron is neglected in the calculations. We found that the results of the GGA calculations show similar volume changes to the experimental data, shown as blue squares in Fig. S1(f).
This result indicates that the changes of the unit cell in the strained LNO films may be an 2 intrinsic property.

S2. Photon-energy scan and kz resolution
The ten-unit cell-thick LNO film has a three-dimensional band structure similar to that of bulk LNO. Therefore, we needed to have a photon-energy scan to identify appropriate photon energies for the two symmetric planes; the ΓXM (ZRA) plane was found to be located at slightly different energies of 150 eV (114 eV) for LNO/LAO, 154 eV (117 eV) for LNO on NdGaO3 (NGO), and 157 eV (120 eV) for LNO/STO due to different lattice parameters. Figure S2 shows the details of the photon energy scan. The thick LNO film has a tetragonal structure under the tensile misfit strain. As shown in Fig. S2(a), the following Brillouin zone (BZ) was represented as a schematic diagram with the symbols for high-symmetry momentum points (Γ, X, M, Z, R, and A). We scanned the photon energy in normal emission, shown as shaded ΓXRZ plane in Fig. S2(a). Figure S2 width at half maximum is around 0.08 Å -1 , which indicates that the scattering lenght is around 25 Å. We note that the reported scattering length of bulk-like LNO under tensile strain is 12 Å [2], which guarantees much better quality of our thin films.

S3. Misfit strain induced changes of the electronic structure in metallic LNO films.
We can explain the misfit strain-induced changes in the band dispersions of the LNO films by considering eg-orbital splitting and changes in the bandwidth W. The two eg orbitals, d3z2-r2 and dx2-y2, are degenerate in a pseudocubic bulk LNO [3]; however, the contraction or elongation of the equatorial Ni−O bond length, dNi−O, due to the misfit strain splits the degenerate eg orbital levels. For example, under compressive strain, the energy level of the d3z2-r2 (dx2-y2) orbital decreases (increases) due to a decreasing (increasing) hybridization with the surrounding oxygen ions [4]. The W of the eg orbitals can also change in response to changes in dNi−O [4]. For instance, under compressive strain, hybridization with apical oxygen ions in the NiO6 octahedra decreases due to an elongation of the Ni−O bond length along the 4 z-direction. Therefore, the W corresponding to the d3z2-r2 orbital is decreased under compressive strain, even though the energy level of that becomes lower.  Figure S7 shows the Fermi-surface topology change more clearly.
However, although the electron band centered at the Γ point has a dominant dx2-y2 orbital character, the band minimum exhibits a slight upward shift with tensile strain. To understand this behavior, the strain-induced change in the W should be also considered. As shown in Fig.   S6, we can clearly observe that the W of the dx2-y2 orbital decreases with tensile strain, although its energy level becomes lower. This indicates that the band minimum at the Γ point may become higher in energy due to the decrease in the W of the dx2-y2 orbital with tensile strain.
We note that the LNO film remains a metallic phase irrespective of misfit strain. There is a result to claim that LNO film might have a gap structure under tensile strain [5]. However, as shown in Fig. S8, we found that the LNO films are metallic, irrespective of misfit strains.
Especially, as shown in Fig. S8(a),(b)-v,vi, the energy-distribution-curves (EDCs) are symmetrized at the EF-crossing points α and β, indicated by red arrows. All the symmetrized 5 EDCs show the peak structure at the EF, which implies the metallic phases of LNO films, not the insulating gap structure.

S4. Fermi-surface superstructures in LNO films.
A careful examination of the FS map in Fig. 3(c)  Thus, to visualize the FS superstructure, we obtained the MDC along the dashed line in Fig.   S9(a). As shown in Fig. S9(b), the MDC shows additional peaks indicated by black arrows.
The peak structure and the peak separation are nearly the same with the hole pocket centered at the A point. This result supports Q = (1/2,1/2,1/2) modulation in FS. Note that, Fig. S10(a) shows a CES map in the ZRA plane of LNO/NGO at a binding energy of 30 meV using a log scale. And figure S10(b) reveals the schematic CES maps after whole BZ folding with Q = (1/2,1/2,1/2). This result indicates that the LNO/NGO has the same FS superstructure with LNO/LAO, as shown in Fig. 4(a).
To investigate the superstructure of the tensile-strained LNO film on STO substrate more clearly, we constructed CES maps in the ΓXM and the ZRA planes at a binding energy of 30 meV using a log scale, as shown in Figs. S11(a) and S11(b). Signal of the FS superstructure in the ZRA plane is quite clear, but that in the ΓXM plane is too weak to notice. Thus, to visualize the FS superstructures, we obtained the MDCs along α and β cuts in the ΓXM and the ZRA planes, respectively, as indicated by dashed lines in Figs. S11(a) and S11(b). The MDCs in the ΓXM and the ZRA planes show the peak structures and the peak separations are nearly the same as shown in Fig. S11(c). The superstructure along the β cut is considered as a 6 replica of the hole pocket at the A point, so that along α cut can originate from the same FS.
This result indicates that the FS superstructure in the tensile-strained LNO film should have a periodic modulation with Q = (1/4,1/4,1/4) for the hole pockets. Note that it cannot be reproduced by a periodic modulation with Q = (1/4,1/4,0), which rules out the possibility of a 2√2 × 2√2 surface reconstruction.

S5. Details of calculation methods.
Calculations of the pseudo-cubic and the strained LNO bulk were performed using a charge-self-consistent DMFT and a full-potential GGA implemented in WIEN2k [6][7][8]. We considered the effects of in-plane strain via a contraction or an elongation of the dNi−O in the NiO6 octahedra. The GGA+DMFT calculations performed with −1.7% strain which had the following lattice constants: a = 3.78 Å and c = 3.88 Å; with +2.0% strain, the lattice constants were a = 3.916 Å and c = 3.798 Å, which shows a consistent behavior with the results of x-ray diffraction measurements. The lattice parameters were optimized with a tolerance of 0.0001 Ry in the GGA calculation. The Perdew-Burke-Ernzerhof parameterization of the GGA (PBE-GGA) [9] was used to treat the exchange correlation because it was able to reproduce pseudo-cubic lattice parameters that were consistent with the experimental values.
In the GGA+DMFT calculations, the local self-energy Σ(ω) of Ni 3d electrons was calculated by solving the corresponding quantum-impurity problem using the continuoustime quantum-Monte-Carlo method at a temperature of 230 K (50 eV -1 ) [10]. The value of the Hubbard U was 14.0 eV, and the Hund's coupling parameter was J = 0.7 eV. Note that the value of U exceeds the conventional value for the rare-earth nickelate system [11][12][13], because a dynamic screening by uncorrelated bands is considered within an energy range of [−10 eV, +10 eV] centered on the Fermi energy. 7 In order to check if any density-wave instabilities exist, Lindhard response functions for the LNO films were calculated. The Lindhard response function [14,15] will show a logarithmic divergence at the q vector corresponding to a wave-vector for charge-or spindensity wave instabilities [16][17][18]. Note that, in the description of the Fermi surface, the GGA+DMFT quasiparticle spectrum shows little deviation from the GGA results. So, we used the GGA eigenvalues for the calculation of the Lindhard response function. The Lindhard response function was calculated from the GGA eigenvalues of random k-points generated by a linear interpolation of a 100 × 100 × 100 k-point grid in the full Brillouin zone, including the Γ point. As the GGA+DMFT quasi-particle spectrum is well defined and shows a little deviation from the GGA results at the Fermi energy, GGA eigenvalues were used for the calculation of the Lindhard response function. As shown in Fig. S12, the susceptibility of LNO with tensile strain has a sharper peak around Q = (1/4,1/4,1/4), compared with that for the compressive strain. Note that the susceptibility, χ(q), are normalized by the value of the χ(0). 8